As he approached his 100th birthday, composer Elliott ­Carter would lie in bed each morning and greet a flood of new musical ideas. He then worked diligently for most of the day, committing thoughts to paper and turning out finished works faster than their world premieres could be scheduled.

For a composer at the century mark to be so prolific, at such a high level, was a phenomenon possibly unique in the history of music. Meanwhile, the works he created seemed to take the diamond-hard, prismatic style of his mature music in directions that were lighter and more fanciful with each passing year.

Mr. Carter died Monday in his New York City home, said his longtime associate, clarinetist Virgil Blackwell. He was 103.

The most respected American composer of the late 20th century, Mr. Carter wrote 158 works and twice received the Pulitzer Prize for music. He was also the first composer to ­receive the National Medal of Arts.

“He was a remarkable man, we know that,” Blackwell said by phone from Manhattan Monday. “Music was the most important thing in his life. He put all of his energy into composing. And the number of pieces he was able to write in the last 10 years was absolutely astounding. They were all different; he didn’t repeat himself.”

Mr. Carter began his career writing in a populist neoclassical style, but beginning with his Cello Sonata of 1948, he moved steadily toward the leading edge of American high modernism. His works of the 1960s, includ­ing the landmark Double Concerto and the hugely ambitious Concerto for Orchestra, established his reputation for music of fierce complexity and uncommon elegance.

The trend of increasing ­intricacy, particularly in the layering of contrasting musical textures that often moved at ­independent speeds, continued in Mr. Carter’s work of the 1970s, including A Symphony of Three Orchestras and the remark­able “Syringa,” in which the two vocal soloists sing in different languages.

Mr. Carter was already in his 80s when he took on the most expansive work of his career, “Symphonia,” and he was 90 when he wrote his first opera, “What Next?” That opera was premiered in 1999, and the question in its title was repeatedly asked of the composer throughout the next decade, as he penned a seemingly endless stream of concertos, brief pieces for orchestra, instrumental chamber music, and vocal works. The scores from this so-called late-late period remained highly challenging, but also, in pieces like the Flute Concerto and the Clarinet Concerto, took on a newly Mozartean level of grace.

Born in New York in 1908, Mr. Carter decided to become a composer after hearing the New York premiere of Stravinsky’s “Rite of Spring,” performed by the work’s first conductor, Pierre Monteux, leading the Boston Symphony Orchestra. He often attended concerts with Charles Ives, who later wrote his recommendation letter for Harvard College, where Mr. Carter studied English as an undergraduate and later received a master’s in music, working with composers Walter Piston and Gustav Holst.

While in Boston, Mr. Carter frequently bought rush tickets for BSO performances and later claimed he learned “the whole repertory of older music” through those concerts in ­Symphony Hall. He also sang with the Harvard Glee Club in performances with the BSO ­under Serge Koussevitzky. After Harvard, Mr. Carter studied in Paris with the doyenne of French music, Nadia ­Boulanger.

Mr. Carter’s more advanced postwar style brought him ­renown, but he still wrestled with the quixotic nature of trying to say something new with a 19th-century instrument, the symphony orchestra itself. The deck was stacked against composers like him, he wrote in 1970, given “the inadequacies of most American performances, the apathy of most conductors and orchestral performers, and the consequent disaffection of audiences.” He remained drawn, however, by the allure of terra incognita.

“If there is still any point in composing for orchestra,” he wrote, “it is to treat the medium with as much novelty of concept as one does harmony, rhythm, or any of the older ­musical methods, so rethought in our time. It is the compositions that are written for ­orchestra that will make it live.”

That novelty of concept in Mr. Carter’s scores drew resistance from some audiences and critics who searched in vain for the core expressive power ­behind the virtuosic musical gearwork. But the composer never lacked for committed champions, who heard in the fractured surfaces of his music a vitality and brilliance resonant with the achievements of great composers past. Among the conductors to most actively champion Mr. Carter’s music have been Daniel Barenboim, Boulez, and former BSO music director James Levine.

“I would have thought that at his age I wouldn’t have felt so sad,” Levine said Tuesday of Mr. Carter’s death. “But it really makes me sad. The force of his energy was so remarkable. I miss it already.”

Levine said Mr. Carter had written a new piece for him that he hopes to premiere as soon as possible. Scored for winds, brass, percussion, and baritone, it is based on a Wallace Stevens poem, from which it takes its ­title, “The American Sublime.”

In recent years, the composer’s music enjoyed a new visibility, thanks in part to the general rise in performance levels, which placed scores once deemed unplayable within the range of ambitious conservatory students. The comparatively lyrical quality of his late-late style also won him new audiences, as did the simple astonishing fact that an artist could reach beyond 100 with his creative powers undimmed.

The BSO commissioned or cocommissioned several of his works, including the Horn Concerto, the Flute Concerto, the “Boston Concerto,” “Interventions,” and “Three Illusions for Orchestra.” The orchestra’s summer music academy, the Tanglewood Music Center, also commissioned several scores, including “Sound Fields” and “Mad Regales.”

Next summer, on Aug. 8, Tanglewood Music Center fellows will perform “Instances,” another cocommissioned work, written earlier this year.

“I feel I owe the Boston ­Symphony a lot,” Mr. Carter told the Globe in 2008, adding, “and I have done what I could to repay them.”

In 1939, Mr. Carter married sculptor Helen Frost-Jones, who died in 2003.

He leaves a son, David of Spencer, Ind., and a grandson.

A memorial service is being planned for next year in New York City.

Mr. Carter’s 100th birthday was marked by a high profile Levine-led BSO program in ­December 2008, performed in Symphony Hall and Carnegie Hall. Many other Boston institutions also joined in the centennial celebrations. The following summer, the Tanglewood Music Center devoted its annual Festival of Contemporary Music to Mr. Carter’s work. This unprecedented tribute included the first performance of Mr. Carter’s “Sound Fields,” led by conductor Stefan Asbury. The music, a study in broad, slowly unfurling chords and gradual shifts in texture, seemed to jolt virtually everyone in Ozawa Hall, as it sounded like nothing Mr. Carter had written before. The composer never lost his ability to surprise.

Mr. Carter was present that week at Tanglewood to attend most of the concerts, often beaming as he stood to acknowledge the ovations from large audiences. In a public inter­view between performances, Mr. Carter said: “These pieces of music, if they spoke ­English instead of notes, they would be very grateful.”